Mean velocity equation for fluctuating flow

Development of a Low Cost and Safe PIV for Mean Flow Velocity and Reynolds Stress Measurements

In this study, a white light particle image velocimetry (WL PIV) system which employs a light sheet generated with a flash was used. The system was developed in order to provide a cost-efficient and safe alternative to laser systems while keeping the accuracy limits required for hydraulic model tests. To investigate the accuracy of WL PIV method under different flow conditions, experiments were...

Mean Velocity Equation for Turbulent Fluid Flow: An Approach via Classical Statistical Mechanics

The possibility to derive an equation for the mean velocity field in turbulent flow by using classical statistical mechanics is investigated. An application of projection operator technique available in the literature is used for this purpose. It is argued that the hydrodynamic velocity defined there, in situations where the fluid is turbulent, is to be interpreted as the mean velocity field; i...

Differential Equation of Sensitivity Matrix for Final Velocity Constraint

A Remark on Soliton Equation of Mean Curvature Flow

with II(X,Y ) = DXY −∇XY, for tangential vector fields X,Y on Σ. We define the mean curvature vector field (in short, MCV) by H = trΣII. In recent years, many people are interested in studying the evolution of the immersion F : Σ → Mn+k along its Mean Curvature Flow (in short, just say MCF). The MCF is defined as follows. Given an one-parameter family of sub-manifolds Σt = Ft(Σ) with immersions...

Flow velocity measurements through a fluctuating free surface by means of adaptive optics

The noninvasive investigation of flows, where media of different optical density participate, is often not possible. A measurement through dynamic water-air surfaces will result in higher measurement uncertainties or they will hinder any measurement at all. To overcome this issue we make use of adaptive optics (AO). Dependent on the measurement system, an adaptive correction of the illumination...